Rotating BPS black holes in matter-coupled AdS4 supergravity

Using the general recipe given in arXiv:0804.0009, where all timelike super-symmetric solutions of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} = 2 $\end{document}, D = 4 gauged supergravity coupled to abelian vector multiplets were classified, we construct genuine rotating supersymmetric black holes in AdS4 with nonconstant scalar fields. This is done for the SU(1, 1)/U(1) model with prepotential F = −iX0X1. In the static case, the black holes are uplifted to eleven dimensions, and generalize the solution found in hep-th/0105250 corresponding to membranes wrapping holomorphic curves in a Calabi-Yau five-fold. The constructed rotating black holes preserve one quarter of the supersymmetry, whereas their near-horizon geometry is one half BPS. Moreover, for constant scalars, we generalize (a supersymmetric subclass of) the Plebanski-Demianski solution of cosmological Einstein-Maxwell theory to an arbitrary number of vector multiplets. Remarkably, the latter turns out to be related to the dimensionally reduced gravitational Chern-Simons action.